Angular function resistor



ec- 1952 K. L. NIELSEN ETAL. 2,621,275

ANGULAR FUNCTION RESISTOR Filed May 6, 1952 2 SHEETS-SHEET 1 INVENTORS: EDWARD/1. ROLA N0 Dec. 9, 1952 K. L. NIELSEN ETAL ANGULAR FUNCTION RESISTOR 2 SHEETS-SHEET 2 Filed May 6, 1952 INVENTORS. EDWARD H. ROLAND KAJ L. N/ELSEN BY/(Q6 a Arrrs Patented Dec. 9, 1952 UNITED ANGULAR FUNCTION RESISTOR Kaj Leo Nielsen and Edward H. Roland, Indianapolis, Ind.

Application May 6, 1952, Serial No. 286,414

(Granted under the act of March 3, 1883, as amended April 30, 1928; 370 0. G. 757) 8 Claims.

This invention relates to a variable resistor. More specifically, it relates to a resistor that may be varied in accordance with the functions of an angle.

In certain installations such as computers it may be desirable to have the angle of a turning member expressed as a resistance that is proportional to some function such as the sine of the angle. Of course, it is possible to accomplish this by the use of a resistor that is not uniform per unit of length or one that is of non-circular shape,

However, there are certain advantages in employing a circular resistance that is uniform per unit of arcuate length. It is accordingly an object of the present invention to adapt such a uniform circular resistor to expressing a resistance proportional to a function of an angle of a turning member.

Other objects and many of the attendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:

Fig. 1 is a schematic view of one form of the present invention;

Fig. 2 is a schematic view of a second form; and

Fig. 3 is a schematic view of a third form.

Fig. 4 is a schematic view of a fourth form.

Fig. 5 shows a wire-wound resistor card.

Fig. 6 is a face view of an actual embodiment of the device shown in Fig. 1.

Fig. 7 is a sectional view taken on the line 1-1 of Fig. 6.

Fig. 8 is a sectional view taken on the line 8--8 of Fig. 7.

In Fig. 1 the reference character I!) designates a resistor of circular shape with a uniform resistance per unit of arcuate length. The resistor should have an arcuate length of 2B degrees. The ends [I and I2 of the resistor are connected by a shunt 13. An arm member I4 is pivotally mounted at a point l5, which is at the middle of the chord l6 between the ends of the resistor. The pivot point is spaced from the center I! of the resistor an amount equal to mr, r being the radius of resistor. The arm member M is adapted to move along the resistor I!) in electrical contact therewith. The values or ranges of values of the angle B and the displacement :cr will be demonstrated.

Applicants have discovered certain optimum values of the displacement :cr of the arm pivot and the angle B at which the effective resistance R of the resistor in is almost exactly directly proportional to the sine of the angle C. They have also discovered certain upper and lower limits for values of .221' and B at which the effective resist- 2 ance will vary no more from the proportionality to the sine of the angle than certain workable percentages, say 5% and 10%.

The efiective resistance R of the device measured between the shunted ends of the resistor l0 and the arm is expressed in the following equation in which R1 is the resistance between the resistor end I l and the arm [4, and R2 is one-half the total resistance between ends H and I2 for a given angle C of the arm measured from the resistor end I l Since R is approximately proportional to the sine of angle C, the following relation is obtained Substituting for g; i

but

Since H is the hypotenuse of a right triangle having sides 1' sin A and scr+r cos A,

sin 0' Substituting for H in (3),

xr-l-r cos A sin C= 3 Substituting for x in (4) and dividing numerator and denominator by r,

'4 Table II V B 1: Minimum I Minimum 0 D C cos A B for 5% error for error 5111 2 5 Vl-l-cos B 2 cos A cos B 90 0 33 .95 .0 52 2 equatin 2) and 5) :l oi 31:1 :8

3 332 1 (A); 00S B (6) 10 7 4 I341; 23:; less gianl 6 58 1 ess an B 1/ 905 A cos B 5 .2750 15.4 less 3115111 7 .2922 ll. 6 less than 1 3 -33 it 3 1 c 958 8.11 In Older to i the optlmum value of h 110-120 34-. 50 less thanl less thanl displacement :nr, 10 is necessary to find the opti- 15 121 .5158 2.0 less 015111 mum value of the angle Bwhich will most nearly 2; satisfy (6) for all values of A. 4 .5592 1%.: ess tgan The best approach to a solution is a method 6 i j 33 ofv successive approximations. Solutions for B 5 22.0 less 1 11 111 are obtained for the values of A spaced 10 de- 9 :6293 grees from one another as indicated in Table I, 130 11428 which follows:

Table I A. 0 10 20 40 50 00 70 so 90 100 110 The arithmetic average value of B is 113.955. Table III The corresponding displacement :01 of the arm I pivot 15 from the resistor center I i is 7 And an 1' cos 113.955=.406019 r If 01 111 0 is a oxim te. 4411051 0 75 no e 5 e ror 1s error is a ow Substituting these values in (6), we obtain: 30 measured for 511515 51315 then 55153119 the angles less the I may be a: may "e in 1 252800829A2 cos A 406019020 anin the interthe interval 7 v 1.164851445+.812038040 cos A an expression, the right hand side of which yields a V the exact value of sin C and the left hand side of o which yields an approximate value of sin C. The 10: 295 2 535 .190 2 700 deviations for the various values of A and the $85 corresponding values of C are given in the fol- 5 5 1E 23 V lowing table. 5 155 I 0 x 50 0 2 1.00 A O differences Percent 0 0 From Table III it may be seen that for a mini- 5,8 0 mum value of one degree for angle 0, variation 0 0 30 68. 5418 0000085 0 of m from .325 to .500 will produce no more than 40 61-2586 0000109 0 5% error, and a variation of :r from .242 to .602 53.8558 0000534 0.01 $8 2329 0001087 0. 02 will produce no more than 10% error,

.5 14 0001442 0.02 80 30. 4815 0001079 M2 Calculations also show that f a: is held to 90 22.0981 0000450 0.01 A1305, the percentage error will be about 3.12 g; 8: 50 at a shade more than one degree for angle C. It 113 .9515 0000849 0.51 angle 0 is increased, the percentage decreases.

jig The arm pivot 15 is at the midpoint of the 113.7 .2548 0000243 0.55 chord [6 between the resistor ends I l and 82 so 8: that the largest value of the efiective resistance 113.955 0 0 R which naturally comes when R1 and R2 are equal, occurs when the angle C is 90 degrees, at

From the foregoing, it is seen that a value of B=113.955 and a value of mr=.4080l9 r are quite satisfactory. Only at very small values of the angle 0 are the percentage errors appreciable, and the errors inherent in small resistances such as those in wire-wound cards far outweigh the theoretical errors.-

Further calculations show that as the minimum value of angle C rises, the reater can be the deviation both up and down from the optimum value of :cr=.406019 r for a given permissible percentage of error; that as the permissible percentage of error rises the greater can be the deviation both up and down from the optimum value of arr for a given minimum value of angle C; that as the minimum value of angle C de creases the percentage error increases for a given value of xr. This may be seen from the rollowing tables I 75 which the sine is of course at a maximum. If the arm member 15 is not to move through an angle as large as degrees, then the arm pivot l5 need not be substantially at the midpoint of the chord 10 between the resistor ends H and i2.

The resistor 50 may take the form of a wirea spacing as described with reference to Fig. 1.

The pivot 15 of the arm member I4 will be at the midpoint of the chord I6 between the points 19 and 20. The arm pivot l5 will be spaced from the resistor center an amount equal to a fraction of the resistor radius as specified wi referent;

to Fig. 1. The effective resistance R will be proportional to the sine of the angle A, as in Fig. 1. The resistor I8 may be formed of a wire-wound card bent to a complete circular cylinder, or the resistor may be of circular shape or circular cylindrical shape formed in any other suitable way. Stops 22 and 23 are provided to keep the arm member l4 on the larger angle of the resistor l8 between points 19 and 20.

In Fig. 3 the resistor is formed of two circular sections 24 and 25, each of the arcuate length described with reference to Fig. 1. The sections have the same radius and the same uniform resistance per unit of arcuate length and are con nected at their ends in junction points 21 and 2B in opposed facing relation with their centers 29 and 39 on opposite sides of the chord 26 connecting the junction points 21 and 28. The pivot l5 of arm member I4 is at the midpoint of chord 26, spaced from each of centers 29 and 39 an amount equal to a fraction of the radius of the sections as specified with reference to Fig. 1. A shunt 31 connects the junction points. The effective resistance R across the shunt 3! and the arm member will be proportional to the sine of the angle A, as in Figs. 1 and 2. In Fig. 3 the arm member may operate over 360 degrees.

In Fig. 4 the arrangement is the same as in Fig. 1 insofar as arcuate length of the resistor I0, location of arm pivot I5, and use of shunt l3 are concerned. However, in Fig. 4 the arm member is replaced by a member 32, which is in effect a pair of rigidly connected arm members extending in opposite directions from the pivot l5. The member 32 enables the device to operate over 360 degrees as in Fig. 3.

Fig. 5 shows a card 35 wound with an enameled resistance wire 36. The enamel is removed from the wire at the top edge of the card. The ends of the winding are anchored in holes 31 in the card 35, and terminal connector portions 39 project therefrom. As shown in Figures 6 and '7, the card 35 is bent to circular shape about a pot 39, which may be formed of a light-weight metal such as aluminum, and is clamped thereto by flange members 49 riveted to the ends of the card as indicated at 4| and by bolts 42 and nuts 43. Pieces 44 are riveted to the ends of the card on the opposite side to the flange members 40. As seen in Fig. 7, the wire-wound card 35 abuts a shoulder 45 at its left end, and its right end projects beyond the pot 39 and is contacted by a contact block 46, having a triangular section, as seen in Fig. 8. The block is secured by screws 41 to the outer end of an arm 49 of this section.

The inner end of the arm 46 is secured by screws 49 to a semi-circular portion 59 of a collar 5!. The collar is clamped to a flanged insulating sleeve 52 on the right end of a shaft 53 by means of lugs 54 on the collar and a screw 55 extending through and into the lugs. The shaft 53 is journaled in a sleeve 56, which is externally threaded to receive clamp nuts 51 and 58 which hold the sleeve in an elongated slot 59 formed in the pot 39. A washer 69 fits between the nut 51 and the pot, and a spacer 6i fits between the nut 53 and the flange on the insulating sleeve 52. The sleeve 56 and the shaft 53 are bodily adjustable transversely of their length in the slot 59 to bring the shaft to an appropriate oifset from the center of the resistor card 35. However, if this offset, which is the amount :rr previously referred to, is determined, the slot can be replaced by a circular opening.

The collar 5| is in sliding electrical contact with a resilient spiral spring member 52 which is wrapped around the collar and is attached to a flanged base member 63 secured by a screw 54 to an insulator block 65 and terminating in a projecting end portion 66. The insulator block is secured by screw 61 to the pct 39. Insulated conductors 68 and 69 lead from the ends 38 (Fig. 5) of the resistance wire 36 and are connected to a terminal screw 10 on the insulator block 65. Conductors 68 and 69 comprise the shunt l3 of Fig. l. Stops H limit the angular movement of the arm 48 and the contact block 46 to the appropriate angle 2B, as discussed with reference to Fig. 1. Three openings 12 spaced degrees from one another about the center of the pot are adapted to receive suitable fastening means that support the pot 39 to another object. It will be seen that the device shown in Figs. 6 and 7 is like the one shown in Fig. 1.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.

The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

We claim:

1. In combination, a circular resistor having an arcuate length greater than and less than 360 degrees and being of equal resistance per unit of arcuate length, means shunting the ends of the resistor and a member angularly movable along the resistor in electrical contact therewith about a pivot located approximately at a midpoint on a straight line connecting the ends of the resistor, the effective resistance across the member and the shunted ends of the resistor being proportional to the sine of the angle subtended by the member and the straight line connecting the ends of the resistor.

2. In combination, a circular resistor having uniform resistance per unit of arcuate length and an arcuate length of about 228 degrees so as to cause the midpoint of a straight line connecting the ends of the resistor to be displaced from the center of the resistor an amount equal to about .406 times the radius of the resistor, means shunting the ends of the resistor, and a member angularly movable along the resistor in electrical contact therewith about a pivot located approximately at said midpoint whereby the effective resistance across the member and the shunted ends of the resistor is proportional to the sine of the angle subtended by the member and the said straight line.

3. In combination, a circular resistor having equal resistance per unit of arcuate length and being shunted across two points spaced more than 180 degrees and a member having a pivot eccentric to the resistor and located at the midpoint of the chord between said two points and being movable in electrical contact with the resistor along the more than 180 degrees between the points.

4. In combination, a circular resistor having uniform resistance per unit of arcuate length and being shunted across two points spaced approximately 218 to 240 degrees, and a member having a pivot spaced from the center of the resistor by approximately .325 to .500 times the radius of the resistorand locatedapproximately at a middle of the chord between said points, the mem ber being'movable in electrical contact with the resistor along'the said 218 to 240 degrees so that the sine of the angle between the chord and the member is approximately proportional to the efiective resistance across the-member and the shunted points of the resistance.

5. In combination, a resistor formed of two circular sections of the sam radius and the same arcuate length greater than 180 and less than 360 degrees and the same equal resistance per unit of arcuate length, the sections being connected through their ends in opposed facing re-- lation with their centers on opposite sides of the chord between their ends, a shunt connecting these ends, and an arm movable along the sections in electrical contact therewith on'a pivot approximately at a midpoint of the said chord, the effective resistance across the member and the shunt being proportional to the sine of the angle subtended by the member and the said chord.

6. In combination, a resistor formed of two circular sections having the same radius and the same uniform resistance per unit of length and the same arcuate length of about 228 degrees, the sections being connected through their ends in opposed facing relation with their centers'cn opposite sides of the chord between their ends an" amount equal to about .406 times the radius, and an arm movable along the sections in electrical contact therewith on a pivot approximately at a midpoint of the said chord.

7. The combination specified in claim 1, the

the resistor and located approximately at a middle of the chord between said points, the member being movable in electrical contact with the re sistor along the said 208 to 254 degrees so that the sine of the angle between the chord and the member is approximately proportional to the efiective resistance across the member and the shunted points of the resistance.

KAJ LEO NIELSEN. EDWARD H. ROLAND.

No references cited. 

